Define the special operation a ⊕ b by the following rules:
⇒ a ⊕ a = a for all positive integers a.
⇒ a ⊕ b = b ⊕ a for all positive integers a and b.
⇒ If a > b ≥ 1, then a ⊕ b = (a - b) ⊕ b.
Compute the value of 16 ⊕ 2018.

Please answer with solution, thanks in advance! :))

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Suprathiksirimilla20viz Suprathiksirimilla20viz · Answer 1

Now, we shall just use the rules given to compute 16 ⊕ 2018.

Using second rule, we can write this as:

2018 ⊕ 16

Use the third rule:

⇒ (2018 - 16) ⊕ 16

Or, since this sequence is continuous, we multiply 127.

⇒ (2018 - (125)16) ⊕ 16

⇒ (2018 - 2000) ⊕ 16

⇒ 18 ⊕ 16

Continue using third rule.

⇒ 18 - 16 ⊕ 16

⇒ 2 ⊕ 16

Use second rule:

⇒ 16 ⊕ 2

Again continue using third rule:

⇒ 16 - 2 ⊕ 2

⇒ 14 - 2 ⊕ 2

⇒ 12 - 2 ⊕ 2

⇒ 10 - 2 ⊕ 2

⇒ 8 - 2 ⊕ 2

⇒ 6 - 2 ⊕ 2

⇒ 4 - 2 ⊕ 2

⇒ 2 ⊕ 2

Here, use the first rule:

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